Design of Compliant Mechanisms of Distributed Compliance Using a Level-Set Based Topology Optimization Method

Abstract:

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This paper presents a level set-based structural shape and topology optimization for the design of compliant mechanisms. The design boundary of the compliant mechanism is implicitly represented as the zero level-set of a higher-dimensional level set surface. A quadratic energy functional is introduced to augment the objective function in order to control the structural geometric size of the resulting mechanism. The optimization is thus changed to a numerical process that describes the design as a sequence of motions by updating the implicit boundaries until the optimized structure is achieved under specified constraints. A semi-implicit scheme with an additive operator splitting (AOS) algorithm is used to solve the Hamilton-Jacobi partial differential equation (PDE) in the level set method. In doing so, it is expected that numerical difficulties in most conventional level set methods can be eliminated. The final mechanism is characterized with strip-like members able to generate distributed compliance, and so that to resolve the hinge problem long sought-after in the design of compliant mechanisms. Typical numerical case is used to evidence the effectiveness of this method in the design of monolithic compliant mechanisms.

Abstract: Compliant mechanisms gain at least some of their mobility from the deflection of flexible members rather than from movable joints only. Dynamic effects are very important to improving the design of compliant mechanisms. An investigation on the dynamics and synthesis of the compliant mechanisms is presented. The dynamic model of compliant mechanisms is developed at first. The natural frequency and sensitivity are then studied based on the dynamic model. Finally, optimal design of compliant mechanism is investigated. The experimental study of natural frequency is performed. The comparison between the experiment results and the theoretical results verifies the validity of the experiment system and theoretical model.

Abstract: This research presents a topology optimization approach based on Bi-directional Evolutionary Structural Optimization (BESO) for optimal design of compliant mechanisms. Due to the complexity of the design for various compliant mechanisms, a new multi-objective optimization model is established by considering the mechanism flexibility and structural stiffness simultaneously. The sensitivity analysis is performed by applying the adjoint sensitivity approach to both the kinematical function and the structural function. The sensitivity numbers are derived according to the variation of the objective function with respect to the design variables. Some numerical examples are given to demonstrate the effectiveness of the proposed method for the design of various compliant mechanisms.

Abstract: Multiple degree-of-freedom compliant mechanisms are widely used in the fields of micro-positioning and micro-manipulation. This paper deals with multiobjective topology optimization of multi-input and multi-output compliant mechanisms undergoing large deformation. The objective function is defined by the minimum compliance and maximum geometric advantage to meet both stiffness and flexibility requirements. The suppression strategy of input and output coupling terms is studied and the expression of the output coupling terms is further developed. The weighted sum of the conflicting objectives resulting from the norm method is used to generate the optimal compromise solutions, and the decision function is set to select the preferred solution. Geometrically nonlinear mechanism response is calculated using the Total-Lagrange finite element formulation and the equilibrium is found using an incremental scheme combined with Newton-Raphson iterations. The solid isotropic material with penalization approach is used in design of compliant mechanisms. The sensitivities of the objective functions are found with the adjoint method and the optimization problem is solved using the Method of Moving Asymptotes. Numerical examples of multiple inputs and outputs are presented to show the validity of the new method. Simulation results show that the compliant mechanisms can be deformed in the desirable manner and the coupling output displacements are suppressed significantly by using the presented method.